Pressure-Dependent Rate Rules for Intramolecular H‑Migration Reactions of Hydroperoxyalkylperoxy Radicals in Low Temperature

Intramolecular H-migration reaction of hydroperoxyalkylperoxy radicals (<sup>•</sup>O<sub>2</sub>QOOH) is one of the most important reaction families in the low-temperature oxidation of hydrocarbon fuels. This reaction family is first divided into classes depending upon H atom transfer from -OOH bonded carbon or non-OOH bonded carbon, and then the two classes are further divided depending upon the ring size of the transition states and the types of the carbons from which the H atom is transferred. High pressure limit rate rules and pressure-dependent rate rules for each class are derived from the rate constants of a representative set of reactions within each class using electronic structure calculations performed at the CBS-QB3 level of theory. For the intramolecular H-migration reactions of <sup>•</sup>O<sub>2</sub>QOOH radicals for abstraction from an -OOH substituted carbon atom (-OOH bonded case), the result shows that it is acceptable to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. For the abstraction from a non-OOH substituted carbon atom (non-OOH bonded case), rate rules for each class are also derived and it is shown that the difference between the rate constants calculated by CBS-QB3 method and rate constants estimated from the rate rules may be large; therefore, to get more reliable results for the low-temperature combustion modeling of alkanes, it is better to assign each reaction its CBS-QB3 calculated rate constants, instead of assigning the same values for the same reaction class according to rate rules. The intramolecular H-migration reactions of <sup>•</sup>O<sub>2</sub>QOOH radicals (a thermally equilibrated system) are pressure-dependent, and the pressure-dependent rate constants of these reactions are calculated by using the Rice–Ramsberger–Kassel–Marcus/master-equation theory at pressures varying from 0.01 to 100 atm. The impact of molecular size on the pressure-dependent rate constants of the intramolecular H-migration reactions of <sup>•</sup>O<sub>2</sub>QOOH radicals has been studied, and it is shown that the pressure dependence of the rate constants of intramolecular H-migration reactions of <sup>•</sup>O<sub>2</sub>QOOH radicals decreases with the molecular size at low temperatures and the impact of molecular size on the pressure-dependent rate constants decreases as temperature increases. It is shown that it is acceptable to derive the pressure-dependent rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. The barrier heights follow the Evans–Polanyi relationship for each type of intramolecular hydrogen-migration reaction studied. All calculated rate constants are fitted by a nonlinear least-squares method to the form of a modified Arrhenius rate expression at pressures varying from 0.01 to 100 atm and at the high-pressure limit. Furthermore, thermodynamic parameters for all species involved in these reactions are calculated by the composite CBS-QB3 method and are given in NASA format.